Wednesday, August 20, 2014

electromagnetism - Displacement current - how to think of it


What is a good way to think of the displacement current? Maxwell imagined it as being movements in the aether, small changed of electric field producing magnetic field. I don't even understand that definition-assuming there is aether. (On the topic of which, has aether actually been disproved? I read that even with the Michelson-Morley experiment the aether wasn't disproved.)



Answer



Maxwell's equations in a vacuum have induction terms. (1) There is a term saying that a time-varying magnetic field produces an electric field. (2) There is a term saying that a time-varying electric field produces a magnetic field.


Among people who insist on giving hard-to-remember names to all the terms in Maxwell's equations, #2 is called the displacement current. The name is a bad one, because it's not a current, i.e., it has nothing to do with the motion of charged, material particles. The only reason it has the misleading name is that it adds to the current term, and Maxwell, who made up the name, wasn't sure what its ultimate origin was.


The importance of term #2 is mainly that it allows the existence of electromagnetic waves. In an electromagnetic wave, the changing E field induces the B field, and the changing B field induces the E field.


There are elementary reasons that term #2 has to exist. For example, suppose you have a circular, flat Amperian surface $S_1$ and you shoot a single charged particle perpendicularly through its center. In this situation, Maxwell's equations without term #2 predict that the magnetic field at the edge of the surface will be zero, then infinite for an instant, and then zero again after that. But if we construct a similar Amperian surface $S_2$ with the same boundary but an interior surface that is bowed out rather than flat, we get a prediction that the infinite field occurs at a different time. This proves that we can't get away with leaving Maxwell's equations in a form with all the terms except term #2.



The deeper reason for term #2 is that it's required by relativity. Only with term #2 do Maxwell's equations have a form that is the same in all frames of reference.


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